Anantecedent is the first half of ahypotheticalproposition, whenever the if-clause precedes the then-clause. In some contexts the antecedent is called theprotasis.^[1]

Examples:

• If${\displaystyle P}$, then${\displaystyle Q}$.

This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent isP, and theconsequent isQ. In theimplication "${\displaystyle \varphi }$ implies${\displaystyle \psi }$",${\displaystyle \varphi }$ is called theantecedent and${\displaystyle \psi }$ is called the consequent.^[2] Antecedent andconsequent are connected vialogical connective to form aproposition.

• If${\displaystyle X}$ is a man, then${\displaystyle X}$ is mortal.

"${\displaystyle X}$ is a man" is the antecedent for this proposition while "${\displaystyle X}$ is mortal" is the consequent of the proposition.

• If men have walked on the Moon, then I am the king of France.

Here, "men have walked on the Moon" is the antecedent and "I am the king of France" is the consequent.

Let${\displaystyle y=x+1}$.

• If${\displaystyle x=1}$ then${\displaystyle y=2}$,.

"${\displaystyle x=1}$" is the antecedent and "${\displaystyle y=2}$" is the consequent of this hypothetical proposition.

• Consequent
• Affirming the consequent (fallacy)
• Denying the antecedent (fallacy)
• Necessity and sufficiency

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